Partial discharge fault diagnosis method for reactor based on compressed sensing and dynamic Bayesian network

Abstract

The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian networks relates to the technical field of fault diagnosis of power equipment, and is used to solve the problem that the existing partial discharge monitoring and fault diagnosis methods of reactors cannot cope with multi-source complex partial discharge signals and environmental noise. The fault diagnosis method of the present invention first uses compressed sensing technology to achieve the sparseness of partial discharge signal characteristics, reduce data redundancy, and retain key features. Subsequently, based on the multi-dimensional partial discharge map technology, the time domain, frequency domain, phase domain and time-frequency domain maps are generated and fused to construct a diversified partial discharge feature representation. The dynamic Bayesian network DBN is used for real-time fault diagnosis, and is optimized by the differential evolution adaptive bacterial foraging optimization DEABFO algorithm to improve the accuracy and efficiency of fault identification. The present invention can effectively cope with multi-source complex partial discharge signals and environmental noise, and is suitable for partial discharge fault prediction and diagnosis under complex working conditions.

Description

Technical Field

[0001] The invention relates to the technical field of power equipment fault diagnosis, and in particular to a reactor partial discharge fault diagnosis method based on compressed sensing and a dynamic Bayesian network. Background Art

[0002] In response to the growing demand for electricity, the installed capacity and voltage level of the power system show a continuous upward trend. While meeting the demand for electricity, it also brings about an increase in reactive power demand and aggravated harmonic pollution. As an important power equipment, dry-type reactors are widely used in power systems to improve power quality due to their good linear characteristics, strong anti-saturation ability and oil-free design. With the increase in reactor capacity and the increase in the number of parallel branches, the probability of turn-to-turn short circuits also increases, which may lead to excessive local temperature rise, further causing insulation damage, and even equipment burning accidents in severe cases. Therefore, under complex working conditions, online fault diagnosis of dry-type reactors has become one of the key technical means to prevent power system operation accidents.

[0003] Partial discharge (PD) is not only one of the key factors leading to insulation aging of electrical equipment, but also an important indicator for measuring insulation degradation. Effective PD monitoring and diagnosis of dry-type reactors can help to detect potential insulation defects early and reduce the risk of equipment failure and loss. The identification of partial discharge patterns, as the core means of evaluating the insulation status of electrical equipment, can provide a reliable diagnostic basis for the insulation performance of dry-type reactors by identifying different types of discharge faults. It is widely used in the status monitoring and health assessment of electrical equipment. Most of the existing partial discharge detection methods are based on a single time domain or frequency domain analysis, which cannot effectively identify complex, multi-source partial discharge signals. Traditional fault identification methods have the problem of insufficient robustness when dealing with noise interference and multi-factor influences. Therefore, it is imperative to develop an intelligent diagnosis method for multi-dimensional partial discharge signal fusion.

[0004] Denoising of partial discharge signals is one of the core issues in power equipment condition monitoring. Traditional methods such as wavelet analysis, modal decomposition and sparse representation have achieved remarkable results in noise suppression. However, sparse representation is mainly applicable to complete measurement data. Its performance is obviously limited under compressed observation conditions, and it is difficult to fully extract signal features. Compressed sensing theory reconstructs signals through a small number of observations, and combined with sparse representation, it can accurately extract partial discharge features under compressed measurement. Compared with traditional methods, compressed sensing not only reduces data requirements, but also maintains signal sparsity under low-dimensional conditions, improves the real-time performance and accuracy of feature extraction, and provides more efficient support for equipment fault diagnosis.

[0005] In the selection of classifiers for partial discharge (PD) pattern recognition, back propagation neural network (BPNN), support vector machine (SVM), K nearest neighbor (KNN) and dynamic Bayesian network (DBN) have been widely used in such tasks. However, these traditional classification methods have their own limitations. Although BPNN has powerful nonlinear mapping capabilities, its training time is long and it is easy to fall into local optimality. The performance of SVM is heavily dependent on parameter selection and it is difficult to process large-scale data. The recognition effect of KNN is easily affected by the K value, and it is difficult to effectively distinguish data of different modes. In contrast, DBN can integrate multi-level information, identify potential dynamic patterns in signals, and provide more comprehensive classification results through its good handling of time dependence and uncertainty. The classic DBN structure learning method still has deficiencies in search efficiency and accuracy of generated networks, especially the lack of a mechanism to escape local optimality during the optimization process, which limits its application in complex fault type recognition. The complex operating environment and diverse fault types of reactors may result in a large amount of abnormal data in the collected PD signals, thereby reducing the classification accuracy of the model. At the same time, the traditional DBN parameter selection method based on manual experience has the problems of subjectivity and inefficiency, which further restricts the classification performance of the model. Summary of the invention

[0006] The purpose of the present invention is to provide a method for partial discharge fault diagnosis of a reactor based on compressed sensing and dynamic Bayesian network, which is used to solve the problem that the existing partial discharge monitoring and fault diagnosis methods of reactors cannot cope with multi-source complex partial discharge signals and environmental noise, and cannot be applied to partial discharge fault prediction and diagnosis under complex working conditions.

[0007] The technical solution adopted by the present invention to solve the technical problem is: a method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network, comprising the following steps:

[0008] S1. Partial discharge signal acquisition.

[0009] The partial discharge signals generated inside the dry-type reactor are monitored and collected in real time through ultra-high frequency sensors, high frequency sensors and ultrasonic sensors.

[0010] S2, compressed sensing denoising.

[0011] S2.1. Express the local discharge signal as a sparse representation.

[0012] In the compressed sensing framework, the PD signal x is expressed by a sparse representation dictionary Ψ, satisfying the following relationship: x = Ψθ (1).

[0013] Among them, θ is the sparse coefficient.

[0014] S2.2. Then, a measurement matrix satisfying the restricted isometry property is selected for compression measurement to generate a low-dimensional compressed observation vector.

[0015] By selecting a measurement matrix Φ that satisfies the restricted equidistance property, the signal is compressed and measured: y=Φθ (2).

[0016] Where y is the compressed observation vector.

[0017] S2.3, then use the orthogonal matching pursuit algorithm OMP to gradually select the basis vector that best matches the current residual, iteratively update the sparse coefficients and calculate the residual until the preset stop condition is met.

[0018] By introducing the sparsity of the signal, it is transformed into solving the sparse coefficient θ.

[0019] y=ΨΦθ=Aθ(3).

[0020] Among them, A=ΦΨ is the perception matrix.

[0021] S2.4. Finally, the obtained sparse coefficients are used to reconstruct the original signal to achieve denoising.

[0022] Using the sparse reconstruction algorithm, the sparse coefficients θ are recovered from the compressed observation vector y and the signal x is further reconstructed.

[0023] S3. Construct a multidimensional graph.

[0024] The time series of the reconstructed signal is analyzed to extract the time domain features, and Fourier transform is used to obtain the frequency domain features. At the same time, a PRPD spectrum is constructed to extract the phase features. The time-frequency analysis technology is used to extract the time-frequency features of the signal, and the features of each domain are integrated to form a comprehensive partial discharge feature representation to support pattern recognition and fault diagnosis.

[0025] S4. Kernelized principal component analysis (KPCA) dimensionality reduction processing.

[0026] Kernelized principal component analysis (KPCA) is used to reduce the dimension of the extracted feature data.

[0027] S5. Dynamic Bayesian network model optimization based on DEBFO algorithm.

[0028] The structure and parameters of the dynamic Bayesian network are optimized by using DEBFO, which is a fusion of two swarm intelligence algorithms: differential evolution DE and bacterial foraging optimization algorithm BFO.

[0029] The bacterial foraging optimization algorithm BFO is subjected to chemotaxis operation. The chemotaxis operation simulates the process of random aggregation of bacteria to the best classification accuracy, which is expressed as follows: (4).

[0030] Where η represents the position vector of the bacteria, J cc It is expressed as the fitness or evaluation index of the bacterial location at the current chemotaxis position, d att represents the attraction depth, ω att represents the attraction width, h rep is the rejection height, ω rep is the exclusion width, η m i represents the mth component of bacteria i, η m represents the mth component of other bacteria in the population. j represents the index of a particular bacterium in the population; k represents the number of chemotaxis steps; and l represents the number of bacterial reproduction steps or generations.

[0031] After the chemotaxis operation, the bacteria enter the reproduction phase, which is described by the following formula: (5).

[0032] in Indicates the health status of bacteria i, which is its fitness value The cumulative sum of .

[0033] In order to prevent the group from falling into the local optimum, the migration operation is introduced into the bacterial foraging optimization algorithm BFO.

[0034] S6. Partial discharge fault diagnosis.

[0035] The optimized DEBFO-DBN model is combined with the high-dimensional features extracted by compressed sensing to perform pattern recognition and fault classification on the partial discharge signal of the dry-type reactor. The dynamic Bayesian network is used to effectively capture the timing characteristics and state transition rules, ultimately achieving accurate classification and real-time diagnosis of different partial discharge fault types.

[0036] Furthermore, various sensors cover signals in different frequency bands to ensure the integrity of multi-dimensional signal data.

[0037] Furthermore, the orthogonal matching pursuit algorithm OMP is selected as the mainstream method of sparse reconstruction. By gradually selecting the basis vectors that best match the residual, the sparse representation of the signal is finally obtained. The solution process is as follows:

[0038] Assume that the number of iterations is t, the residual is r, and the index set is S=[s1,s2,…,s t ], the sparse coefficient is θ=[θ1,θ2,…,θ t ], set the residual threshold to ϵ; initialize the residual r0=y, the sparse coefficient θ0=0, and the index set S0= , atomic matrix A0= , iteration counter t=1.

[0039] In each iteration, the index s corresponding to the atom that best matches the current residue is selected t , determined by the following formula: (6).

[0040] Among them, ϕ j The jth column of the perception matrix Φ is selected as the index s t Add index set S and update atomic matrix A t :

[0041] (7).

[0042] Solve the sparse coefficients according to the least squares method so that the observed value y and the atomic matrix A t The linear combination error is minimal: (8).

[0043] Which resolves to: (9).

[0044] A T t is the atomic matrix A t The transpose of .

[0045] Update the residual according to the current sparse coefficients: (10).

[0046] When the residual r t When the norm of is less than the preset threshold ϵ, the iteration is stopped and the sparse coefficients are finally obtained. The sparse coefficients and the dictionary Ψ are used to reconstruct the original signal through formula (1), thereby achieving sparse reconstruction of the original signal.

[0047] Furthermore, the specific steps of step S3 are:

[0048] S3.1. By analyzing the time series of the reconstructed signal, the time domain features of peak value, pulse duration and discharge number are extracted.

[0049] S3.2. Apply Fourier transform to convert the reconstructed signal from time domain to frequency domain, extract the frequency domain characteristics of spectrum energy, center frequency and bandwidth to reveal the frequency structure and energy distribution of the signal.

[0050] S3.3. By analyzing the phase characteristics of the partial discharge signal relative to the power system power frequency voltage, a two-dimensional PRPD map of phase-discharge intensity is constructed to reveal the correlation between the discharge intensity and the phase angle.

[0051] S3.4. Use time-frequency analysis technology to extract signal features in both time and frequency dimensions, generate time-frequency spectra, and capture the dynamic changes of local discharge signals in instantaneous frequency and energy distribution.

[0052] S3.5. Integrate the time domain, frequency domain, phase domain and time-frequency domain features to form a multi-dimensional partial discharge feature representation, comprehensively characterize the key characteristics of the signal after compressed sensing, and provide efficient and accurate data support for partial discharge pattern recognition and fault diagnosis.

[0053] Furthermore, the content of step S4 is:

[0054] S4.1. Kernelized principal component analysis (KPCA) maps the sample space to a high-dimensional space through a kernel function and calculates the principal components in the high-dimensional space.

[0055] S4.2, according to the cumulative contribution rate of the characteristic value r1, ..., r n And a given threshold h, the first n principal components are selected to form the optimal feature set.

[0056] S4.3. Feature selection is performed after feature fusion. Vectorized representation is generated by combining important features and used for model training.

[0057] Furthermore, the specific steps of the dynamic Bayesian network DBN are as follows:

[0058] First, determine the initial state variable set X0 of the system and construct the initial network B0; the initial network B0 describes the state of the system at time t=0 through the joint probability distribution P(X0).

[0059] Next, define the transition network B between time steps t and t+1 → , to reflect the time evolution of the system state.

[0060] After establishing the initial network B0 and the transition network B → After that, through the joint probability distribution P(X0,X1,…,X T ) models the global state of the system from time t=0 to t=T, and the joint probability distribution is: (11) .

[0061] represents the distribution of the initial state, is the conditional probability at time t given all previous states.

[0062] Furthermore, in the dynamic Bayesian network DBN, the Markov assumption is used to simplify the model, that is, it is assumed that at any time t, the state X at time t+1 t+1 Depends only on X at the current moment t , and is independent of other previous state conditions, simplifying to: (12).

[0063] It is further assumed that the network topology and conditional probability distribution do not change over time between adjacent time steps, that is, It has nothing to do with time t.

[0064] Furthermore, the steps of the migration operation are as follows: through random migration, some bacteria will randomly choose new positions to increase the exploration range of the solution space; migration occurs with a certain probability Ped, and the migrated bacteria are randomly relocated; after a period of search, bacteria with higher classification accuracy are copied, and individuals with lower classification accuracy are eliminated; then, by setting the migration probability, bacteria migrate randomly.

[0065] Furthermore, the specific improvement steps of differential evolution DE include:

[0066] (1) Chemotaxis operation.

[0067] The chemotaxis operation introduces the bacterial sensitivity V to sense the global optimal position and accelerates the convergence speed by adaptive step size adjustment, which is expressed by expressions (13)-(14).

[0068] (13).

[0069] (14).

[0070] Among them, V represents the sensitivity of bacteria to the global optimal solution; is the fitness value of the current bacteria; is the maximum fitness value in the population; parameter and The upper and lower limits of the optimization search space are defined respectively; is the generated random number; C(i) new represents the updated step size of the bacteria in the chemotaxis operation; C(i) is the current step size of the bacteria; step max is the maximum allowed step size defined; step i represents the actual step taken by the bacteria in the i-th iteration.

[0071] (2) Mutation operation.

[0072] In the mutation operation of differential evolution, two individuals X2(t) and X3(t) different from the current individual X1(t) are first randomly selected from the population, and a differential vector is generated by calculating their vector difference, which is then multiplied by the scaling factor F for adjustment, as shown in expression (15).

[0073] (15).

[0074] (3) Crossover operation.

[0075] The crossover operation controls the gene exchange between individuals through the crossover factor CR ori. During this process, a dimension irand is randomly selected for forced crossover, and whether to exchange genes in other dimensions is determined based on the value of the random number rand, as shown in expression (16).

[0076] (16).

[0077] Among them, CR is the crossover factor, which is used to control the probability of gene exchange between individuals; irand represents the randomly selected dimension index to ensure mandatory crossover on a specific dimension; rand is a generated random number, usually in the range of [0, 1], which is used to determine whether to perform a crossover operation on a non-mandatory dimension.

[0078] (4) Select an operation.

[0079] The selection operation adopts a greedy strategy, which determines the retention of individuals by comparing the fitness values ​​of the offspring individual X1(t+1) and the parent individual X1(t); if the fitness of the offspring individual is better than that of the parent, the offspring individual is retained as the parent of the next generation; otherwise, the original parent individual is retained.

[0080] The beneficial effects of the present invention are as follows: the present invention first uses compressed sensing technology to achieve the sparseness of local discharge signal characteristics, reduce data redundancy, and retain key features. Subsequently, based on the multi-dimensional local discharge map technology, the time domain, frequency domain, phase domain and time-frequency domain maps are generated and fused to construct a diversified local discharge feature representation. Real-time fault diagnosis is performed through the dynamic Bayesian network DBN model, and the DEABFO algorithm is optimized through differential evolution adaptive bacterial foraging optimization to improve the accuracy and efficiency of fault identification. The present invention can effectively deal with multi-source complex local discharge signals and environmental noise, and is suitable for local discharge fault prediction and diagnosis under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a diagram of the theoretical framework of compressed sensing.

[0082] Figure 2 This is a diagram of the dynamic Bayesian network model.

[0083] Figure 3 This is the flow chart of the dynamic Bayesian network.

[0084] Figure 4 This is the flow chart of the DEABFO algorithm.

[0085] Figure 5 Improve some flowcharts for differential evolution.

[0086] Figure 6 It is a framework diagram of the present invention. DETAILED DESCRIPTION

[0087] like Figure 6 As shown, the reactor partial discharge fault diagnosis method based on compressed sensing and dynamic Bayesian network of the present invention comprises the following steps:

[0088] S1. Partial discharge signal acquisition.

[0089] The local discharge signals generated inside the dry-type reactor are monitored and collected in real time through ultra-high frequency sensors, high frequency sensors and ultrasonic sensors; the above-mentioned sensors cover signals in different frequency bands to ensure the integrity of multi-dimensional signal data.

[0090] S2, compressed sensing denoising.

[0091] like Figure 1 As shown in the figure, compressed sensing theory uses the sparse characteristics of signals to achieve efficient compressed measurement, data transmission and signal reconstruction. In the application of partial discharge signal processing, compressed sensing significantly improves the efficiency of signal acquisition and processing through sparse representation and reconstruction algorithms. Compressed sensing mainly consists of the following three steps: selection of measurement matrix, construction of sparse dictionary and design of reconstruction algorithm.

[0092] S2.1. Express the local discharge signal as a sparse representation.

[0093] In the compressed sensing framework, the partial discharge signal x is expressed by the sparse representation dictionary Ψ, satisfying the following relationship:

[0094] (1).

[0095] Among them, θ is a sparse coefficient, most of whose elements are close to zero, indicating the sparse representation of the signal in the dictionary Ψ. Each column vector of the dictionary Ψ is called an atom, which aims to describe the characteristics of the PD signal.

[0096] S2.2. Then, a measurement matrix satisfying the restricted isometry property RIP is selected for compression measurement to generate a low-dimensional compressed observation vector.

[0097] By selecting the measurement matrix Φ that satisfies the restricted isometry property RIP, the signal is compressed and measured:

[0098] (2).

[0099] Where y is the compressed observation vector, whose dimension is much smaller than the dimension of the original signal x. This feature means that after compression at the sensor level, only a small amount of compressed observation vector y needs to be transmitted. Since the dimension of the compressed observation vector y is lower than that of the original signal x, directly solving x becomes an underdetermined problem.

[0100] S2.3, then use the orthogonal matching pursuit algorithm OMP to gradually select the basis vector that best matches the current residual, iteratively update the sparse coefficients and calculate the residual until the preset stop condition is met.

[0101] By introducing the sparsity of the signal, the problem is transformed into solving the sparse coefficient θ: (3).

[0102] in, is the perception matrix.

[0103] S2.4. Finally, the obtained sparse coefficient θ is used to reconstruct the original signal to achieve denoising.

[0104] Using the sparse reconstruction algorithm, the sparse coefficient θ is recovered from the compressed observation vector y, and the signal x is further reconstructed. The orthogonal matching pursuit algorithm OMP (Orthogonal Matching Pursuit) is selected as the mainstream method of sparse reconstruction. By gradually selecting the basis vector that best matches the residual, the sparse representation of the signal is finally obtained. The solution process is as follows:

[0105] Assume that the number of iterations is t, the residual is r, and the index set is S=[s1,s2,…,s t ], the sparse coefficient is θ=[θ1,θ2,…,θ t ], set the residual threshold to ϵ. Initialize the residual r0=y, sparse coefficient θ0=0, index set S0= , atomic matrix A0= , iteration counter t=1.

[0106] In each iteration, the index s corresponding to the atom that best matches the current residue is selected t , determined by the following formula:

[0107] (4).

[0108] Among them, ϕ j is the jth column of the perception matrix Φ, and the selected index s t Add index set S and update atomic matrix A t :

[0109] (5).

[0110] According to the least squares method, the sparse coefficient θ is solved so that the compressed observation vector y and the atomic matrix A t The linear combination error is minimal:

[0111] (6).

[0112] Which resolves to:

[0113] (7).

[0114] A T t is the atomic matrix A t The transpose of .

[0115] Update the residual according to the current sparse coefficient θ:

[0116] (8).

[0117] When the residual r t When the norm of is less than the preset threshold ϵ, the iteration is stopped, and the sparse coefficient θ is finally obtained. The sparse coefficient θ and the dictionary Ψ are used to reconstruct the original signal through formula (1), thereby realizing the sparse reconstruction of the original signal.

[0118] S3. Construct a multidimensional graph.

[0119] The time series of the reconstructed signal is analyzed to extract the time domain features, and the frequency domain features are obtained by Fourier transform, while the PRPD spectrum is constructed to extract the phase features. The time-frequency analysis technology is used to extract the time-frequency features of the signal, and the features of each domain are integrated to form a comprehensive partial discharge feature representation to support pattern recognition and fault diagnosis. Specifically:

[0120] S3.1. By analyzing the time series of the reconstructed signal, the time domain features of peak value, pulse duration and discharge number are extracted.

[0121] S3.2. Apply Fourier transform to convert the reconstructed signal from time domain to frequency domain, extract the frequency domain characteristics of spectrum energy, center frequency and bandwidth to reveal the frequency structure and energy distribution of the signal.

[0122] S3.3. By analyzing the phase characteristics of the partial discharge signal relative to the power system power frequency voltage, a two-dimensional PRPD map of phase-discharge intensity is constructed to reveal the correlation between the discharge intensity and the phase angle.

[0123] S3.4. Use time-frequency analysis techniques, such as short-time Fourier transform or wavelet transform, to extract signal features in both time and frequency dimensions, generate time-frequency spectra, and capture the dynamic changes of local discharge signals in instantaneous frequency and energy distribution.

[0124] S3.5. Integrate the time domain, frequency domain, phase domain and time-frequency domain features to form a multi-dimensional partial discharge feature representation, comprehensively characterize the key characteristics of the signal after compressed sensing, and provide efficient and accurate data support for partial discharge pattern recognition and fault diagnosis.

[0125] S4. Kernelized principal component analysis (KPCA) dimensionality reduction processing.

[0126] In order to solve the interference of redundant and irrelevant features on model training during feature extraction, kernelized principal component analysis KPCA is used to reduce the dimension of the extracted feature data. Through kernelized principal component analysis KPCA, highly correlated redundant features are reduced, thereby reducing model complexity and shortening training time. The specific steps are:

[0127] S4.1. Kernelized principal component analysis (KPCA) maps the sample space to a high-dimensional space through a kernel function and calculates the principal components in the high-dimensional space.

[0128] S4.2, according to the cumulative contribution rate of the characteristic value r1, ..., r n And a given threshold h, the first n principal components are selected to form the optimal feature set.

[0129] S4.3. Feature selection is performed after feature fusion. Vectorized representation is generated by combining important features and used for model training.

[0130] S5. Dynamic Bayesian network model optimization based on DEBFO algorithm.

[0131] In order to improve the accuracy of partial discharge fault diagnosis, DEBFO is used to optimize the structure and parameters of the dynamic Bayesian network. By integrating the advantages of DE and BFO, two swarm intelligence algorithms, DEBFO realizes global optimization search of the structure and parameters of the dynamic Bayesian network, and enhances the model's adaptability to complex dynamic nonlinear signals. The optimized dynamic Bayesian network DBN model can accurately capture the complex spatiotemporal dependence characteristics of the partial discharge process, and improve its processing effect on nonlinear and multimodal signals by adaptively adjusting parameters and network structure, significantly improving the accuracy and robustness of partial discharge fault diagnosis.

[0132] The Bayesian network N is a binary pair N=(G,θ), which includes the structure G and the network parameter θ. The independent relationship between a set of variables can be represented by a directed acyclic graph DAG. G=(X,E) represents a specific instance or representation of the directed acyclic graph DAG, where X is a non-empty set of all nodes in the directed acyclic graph DAG, represented by X={X1,X2,...,X i ,...,X n}, each X i It can be an observed variable or a latent variable; E is the set of directed line segments between different variables in the directed acyclic graph DAG, representing the direct dependency relationship between nodes, as shown in formula (9).

[0133] (9).

[0134] Among them, pa(X i) is the parent node set of node X; given the parent node set pa(X i ), according to Markov independence, node X i and its non-descendant node set nd(X i ) are independent. Therefore, several nodes X that follow the Markov rule i The joint probability can be expressed as:

[0135] (10).

[0136] Each node X i In the known parent node set pa(X i ) is composed of the network parameters θ={θ1,θ2,...,θ n}. When the network structure G and network parameters θ of the Bayesian network are known, the node X can be calculated. i The joint probability distribution of . Compared with other methods for calculating joint probability, the Bayesian network algorithm has significantly higher computational efficiency due to the conditional independence between nodes. However, when dealing with the fault diagnosis problem of partial discharge signals of reactors, it cannot cope with the time dependency of data and the processing of complex multidimensional data.

[0137] Dynamic Bayesian Networks (DBNs) illustrate the conditional independence relationship between random variables and their time evolution patterns, such as Figure 2 The dynamic Bayesian network DBN model shown in the figure has a unique transition network that can reflect the state changes of the system under different environmental factors at different time points, showing the complex interactions and dependencies between variables in the system, which is closer to the actual situation of dynamic multidimensional time series data than the Bayesian network.

[0138] like Figure 3 As shown, the specific steps of the dynamic Bayesian network DBN are as follows:

[0139] First, determine the initial state variable set X0 of the system and construct the initial network B0. The initial network B0 describes the state of the system at time t=0 through the joint probability distribution P(X0). The initial network B0 defines the dependency relationship between the variables of the system, laying the foundation for the time series inference of the dynamic Bayesian network DBN.

[0140] Next, define the transition network B between time steps t and t+1 → , to reflect the time evolution of the system state. Transition network B → The core of the conditional probability distribution P(X t+1 ∣X t ), describes how the system state at the current time t affects the state at the next time t+1.

[0141] After establishing the initial network B0 and the transition network B → After that, through the joint probability distribution P(X0,X1,…,X T ) models the global state of the system from time t=0 to t=T. The joint probability distribution is:

[0142] (11).

[0143] represents the distribution of the initial state, is the conditional probability at time t given all previous states.

[0144] To simplify the model, the Markov assumption is used, that is, assuming that at any time t, the state X at time t+1 t+1 Depends only on X at the current moment t , and is independent of other previous state conditions. This assumption simplifies to:

[0145] (12).

[0146] It is further assumed that the network topology and conditional probability distribution do not change over time between adjacent time steps, that is, It is independent of time t, which helps to improve the robustness and scalability of the model and reduce the complexity of structural learning.

[0147] In order to improve the efficiency and accuracy of learning dynamic Bayesian network structures, it is necessary to use swarm intelligence algorithms for optimization. By generating and selecting new populations at each time step, the Bayesian network structure is optimized so that it can adapt to changes in the dynamic environment. The process starts with the initial network B0 and passes through the transition network B → Iteratively adjust the network structure.

[0148] The bacterial foraging optimization algorithm BFO achieves optimal parameter search by simulating the foraging behavior of Escherichia coli. It has the advantages of being insensitive to initial values ​​and avoiding premature convergence, and has been well applied in many fields. The bacterial foraging optimization algorithm BFO is a global random search algorithm. The simulation of bacterial populations includes four steps: chemotaxis, clustering, reproduction, and elimination of dispersion. Figure 4 As shown in the figure. The characteristics of the bacterial foraging optimization algorithm BFO are that it does not require the gradient information of the optimization object during the optimization process, has low complexity and fast convergence speed, can reduce the number of iterations, jump out of the local optimum and find the global optimal DBN structure with the highest score. However, the original bacterial foraging optimization algorithm BFO also has certain defects, such as the randomness of the step size in chemotaxis, the poor information exchange of the clustering mechanism, and the inability to maintain a balance between global and local searches.

[0149] The bacterial foraging optimization algorithm BFO of the present invention is based on the chemotaxis, reproduction and migration behavior of bacteria. It searches and updates the complex solution space through the fitness distribution to achieve population evolution and optimize the dynamic Bayesian network DBN structure parameters, thereby improving the accuracy of partial discharge classification.

[0150] Chemotaxis is a process that simulates random aggregation of bacteria to achieve the best classification accuracy, including rolling and swimming behaviors. In addition, the process also involves aggregation behavior between bacteria, which is expressed as follows:

[0151] (13).

[0152] Where η represents the position vector of the bacteria, J cc It is expressed as the fitness or evaluation index of the bacterial location at the current chemotaxis position, d att represents the attraction depth, ω att represents the attraction width, h rep is the rejection height, ω rep is the exclusion width, η m i represents the mth component of bacteria i, η m represents the mth component of other bacteria in the population. Usually, d att =h rep j represents the index of a particular bacterium in the population; k represents the number of chemotaxis steps; and l represents the number of bacterial reproduction steps or generations.

[0153] After a certain chemotactic operation, the bacteria enter the reproduction stage, which is described by the following formula: (14).

[0154] in Indicates the health status of bacteria i, which is its fitness value The cumulative sum of . When bacteria with better health meet the conditions, they will replicate to form new individuals, while bacteria that are not fit to survive will be eliminated. The reproduction operation ensures that individuals with higher fitness can survive and reproduce in the population, thereby improving the fitness level of the entire group and avoiding falling into the local optimum too early.

[0155] In order to prevent the group from falling into the local optimum, the migration operation is introduced into the bacterial foraging optimization algorithm BFO. Through random migration, some bacteria will randomly choose new positions to increase the exploration range of the solution space. Migration occurs with a certain probability Ped, and the migrated bacteria are randomly relocated. After a period of search, in order to improve the search accuracy and efficiency, bacteria with higher classification accuracy are copied, and individuals with lower classification accuracy are eliminated. Subsequently, by setting the migration probability, bacteria migrate randomly. Although migration interrupts the chemotaxis process, the new individuals randomly generated by the migration behavior may be closer to the global optimal solution of the dynamic Bayesian network structure, which is conducive to further exploring the bacterial population with the highest classification accuracy.

[0156] Differential evolution DE, as a random parallel search algorithm, is often used for optimization problems in complex environments due to its excellent global convergence and robustness. In view of the problem that the bacterial foraging optimization algorithm BFO is prone to fall into local optimality and slow convergence, the differential evolution DE of the present invention enhances the global exploration ability of the solution space through the improvement of mutation and crossover mechanisms, avoiding premature convergence to suboptimal solutions. At the same time, the efficient parallel search characteristics of differential evolution DE speed up the optimization process, thereby solving the problems of local convergence and low convergence efficiency of the bacterial foraging optimization algorithm BFO in complex optimization problems.

[0157] The specific improvement steps of differential evolution DE of the present invention are as follows: Figure 5 As shown, including:

[0158] (1) Chemotaxis operation.

[0159] The core chemotaxis operation of the bacterial foraging optimization algorithm BFO depends on the walking step size C, which controls the convergence and diversity of the group. If C is too small, the search range of bacteria is limited and it is difficult to find the global optimal solution; if C is too large, it may cause bacteria to cross the optimal area and fall into the local optimum. On this basis, the chemotaxis operation introduces the bacterial sensitivity V to perceive the global optimal position, and accelerates the convergence speed by adaptive step size adjustment, which is expressed by expressions (15)-(16).

[0160] (15).

[0161] (16).

[0162] Among them, V represents the sensitivity of bacteria to the global optimal solution; is the fitness value of the current bacteria; is the maximum fitness value in the population; parameter and The upper and lower limits of the optimization search space are defined respectively; is the generated random number; C(i) newrepresents the updated step size of the bacteria in the chemotaxis operation; C(i) is the current step size of the bacteria; step max is the maximum allowed step size defined; step i represents the actual step taken by the bacteria in the i-th iteration.

[0163] (2) Mutation operation.

[0164] In the mutation operation of differential evolution, two individuals X2(t) and X3(t) in the population that are different from the current individual X1(t) are first randomly selected, and the difference vector is generated by calculating their vector difference, and then multiplied by the scaling factor F for adjustment, as shown in expression (17). This step is intended to introduce population diversity and expand the search space, thereby ensuring that the algorithm can fully explore the possibility of different solutions.

[0165] (17).

[0166] (3) Crossover operation.

[0167] The crossover operation controls the gene exchange between individuals through the crossover factor CR. In this process, a dimension irand is randomly selected for forced crossover, and the value of the random number rand determines whether to exchange genes in other dimensions, as shown in expression (18). This step is used to retain the excellent characteristics of individuals and promote the diversification of the population.

[0168] (18).

[0169] Among them, CR is the crossover factor, which is used to control the probability of gene exchange between individuals; irand represents the randomly selected dimension index to ensure mandatory crossover on a specific dimension; rand is a generated random number, usually in the range of [0, 1], which is used to determine whether to perform a crossover operation on a non-mandatory dimension.

[0170] (4) Select an operation.

[0171] The selection operation adopts a greedy strategy, which determines the retention of individuals by comparing the fitness values ​​of the offspring individual X1(t+1) and the parent individual X1(t). If the fitness of the offspring individual is better than that of the parent, the offspring individual is retained as the parent of the next generation; otherwise, the original parent individual is retained. This strategy ensures that the population gradually evolves towards a better solution.

[0172] S6. Partial discharge fault diagnosis.

[0173] The optimized DEBFO-DBN model is combined with high-dimensional features extracted by compressed sensing to perform pattern recognition and fault classification on the partial discharge signal of dry-type reactors. The dynamic Bayesian network effectively captures the timing characteristics and state transition rules, and ultimately achieves accurate classification and real-time diagnosis of different partial discharge fault types.

[0174] The present invention first uses compressed sensing technology to achieve the sparseness of local discharge signal features, reduce data redundancy, and retain key features. Subsequently, based on the multidimensional local discharge map technology, the time domain, frequency domain, phase domain and time-frequency domain maps are generated and fused to construct a diversified local discharge feature representation. Real-time fault diagnosis is performed through the dynamic Bayesian network DBN model, and the DEABFO algorithm is optimized through differential evolution adaptive bacterial foraging optimization to improve the accuracy and efficiency of fault identification. The present invention can effectively deal with multi-source complex local discharge signals and environmental noise, and is suitable for local discharge fault prediction and diagnosis under complex working conditions.

Claims

1. A method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian networks, characterized in that: The following steps are involved: S1. Partial discharge signal acquisition The partial discharge signals generated inside the dry-type reactor are monitored and collected in real time through ultra-high frequency sensors, high frequency sensors and ultrasonic sensors; S2, compressed sensing denoising S2.1, expressing the partial discharge signal as a sparse representation; In the compressed sensing framework, the partial discharge signal x is expressed by the sparse representation dictionary Ψ, satisfying the following relationship: x=Ψθ (1) Among them, θ is the sparse coefficient; S2.2, then select a measurement matrix that satisfies the restricted isometry property for compression measurement to generate a low-dimensional compressed observation vector y; By selecting a measurement matrix Φ that satisfies the restricted equidistance property, the signal is compressed and measured: y=Φθ (2) Where y is the compressed observation vector; S2.3, then use the orthogonal matching pursuit algorithm OMP to gradually select the basis vector that best matches the current residual, iteratively update the sparse coefficient θ and calculate the residual until the preset stop condition is met; By introducing the sparsity of the signal, it is transformed into solving the sparse coefficient θ: y=ΨΦθ=Aθ (3) Among them, A = ΨФ is the perception matrix; S2.4, finally, the original signal is reconstructed using the obtained sparse coefficients to achieve denoising; Using the sparse reconstruction algorithm, the sparse coefficients θ are recovered from the compressed observation vector y, and the signal x is further reconstructed; S3. Building a multidimensional graph Analyze the time series of the reconstructed signal to extract time domain features, use Fourier transform to obtain frequency domain features, and construct a PRPD spectrum to extract phase features. Use time-frequency analysis technology to extract the time-frequency features of the signal, and fuse the features of each domain to form a comprehensive partial discharge feature representation to support pattern recognition and fault diagnosis. S4. Kernelized principal component analysis (KPCA) dimensionality reduction Kernelized principal component analysis KPCA is used to reduce the dimension of the extracted feature data; S5. Dynamic Bayesian Network Model Optimization Based on DEBFO Algorithm The structure and parameters of the dynamic Bayesian network DBN are optimized by using DEBFO, which is a fusion of two swarm intelligence algorithms: differential evolution DE and bacterial foraging optimization algorithm BFO. The bacterial foraging optimization algorithm BFO is subjected to chemotaxis operation. The chemotaxis operation simulates the process of random aggregation of bacteria to the best classification accuracy, which is expressed as follows: Where η represents the position vector of the bacteria, J cc It is expressed as the fitness or evaluation index of the bacterial location at the current chemotaxis position, d att represents the attraction depth, ω att represents the attraction width, h rep is the rejection height, ω rep is the exclusion width, η m i represents the mth component of bacteria i, η m The mth component representing other bacteria in the population; After the chemotaxis operation, the bacteria enter the reproduction phase, which is described by the following formula: in represents the health status of bacteria i, which is its fitness value J(η i (k)) cumulative sum; Introducing migration operation into the bacterial foraging optimization algorithm BFO; S6. Partial discharge fault diagnosis The optimized DEBFO-DBN model is combined with the high-dimensional features extracted by compressed sensing to perform pattern recognition and fault classification on the partial discharge signal of the dry-type reactor. The dynamic Bayesian network is used to capture the timing characteristics and state transition rules, ultimately achieving accurate classification and real-time diagnosis of different partial discharge fault types.

2. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1 is characterized in that: Ultra-high frequency sensors, high frequency sensors and ultrasonic sensors cover signals in different frequency bands respectively to ensure the integrity of multi-dimensional signal data.

3. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1 is characterized in that: The orthogonal matching pursuit algorithm OMP is selected as the mainstream method of sparse reconstruction. By gradually selecting the basis vectors that best match the residual, the sparse representation of the signal is finally obtained. The solution process is as follows: Assume that the number of iterations is t, the residual is r, and the index set is S = [s1, s2, ..., s t ], the sparse coefficient vector is θ=[θ1,θ2,…,θ t ], set the residual threshold to ∈; initialize the residual r0 = y, the sparse coefficient θ0 = 0, and the index set Atomic Matrix Iteration counter t=1; In each iteration, the index s corresponding to the atom that best matches the current residue is selected t , determined by the following formula: Among them, φ j is the jth column of the perception matrix Φ, and the selected index s t Add index set S and update atomic matrix A t : Solve the sparse coefficients according to the least squares method so that the compressed observation vector y and the atomic matrix A t The linear combination error is minimal: Which resolves to: A T t is the atomic matrix A t The transpose of Update the residual according to the current sparse coefficients: When the residual r t When the norm of is less than the preset threshold ∈, the iteration is stopped, and finally the sparse coefficients are obtained. The sparse coefficients and the dictionary Ψ are used to reconstruct the original signal through formula (1), thereby realizing the sparse reconstruction of the original signal.

4. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1, characterized in that: The specific steps of step S3 are: S3.1, by analyzing the time series of the reconstructed signal, extracting the time domain features of peak value, pulse duration and discharge number; S3.

2. Apply Fourier transform to convert the reconstructed signal from time domain to frequency domain, extract the frequency domain features of spectrum energy, center frequency and bandwidth to reveal the frequency structure and energy distribution of the signal; S3.3, by analyzing the phase characteristics of partial discharge signals relative to the power system power frequency voltage, a two-dimensional PRPD map of phase-discharge intensity is constructed to reveal the correlation between discharge intensity and phase angle; S3.

4. Use time-frequency analysis technology to extract signal features in both time and frequency dimensions, generate time-frequency spectra, and capture the dynamic changes of partial discharge signals in instantaneous frequency and energy distribution; S3.

5. Integrate the time domain, frequency domain, phase domain and time-frequency domain features to form a multi-dimensional partial discharge feature representation, comprehensively characterize the key characteristics of the signal after compressed sensing, and provide efficient and accurate data support for partial discharge pattern recognition and fault diagnosis.

5. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1, characterized in that: The content of step S4 is: S4.

1. Kernelized principal component analysis KPCA maps the sample space to a high-dimensional space through a kernel function and calculates the principal components in the high-dimensional space; S4.2, according to the cumulative contribution rate of the characteristic value r1, ..., r n And a given threshold h, select the first n principal components to form the optimal feature set; S4.

3. Feature selection is performed after feature fusion. Vectorized representation is generated by combining important features and used for model training.

6. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1, characterized in that: The specific steps of the dynamic Bayesian network DBN are as follows: First, determine the initial state variable set X0 of the system and construct the initial network B0; the initial network B0 describes the state of the system at time t=0 through the joint probability distribution P(X0); Next, define the transition network B between time steps t and t+1 → , to reflect the time evolution of the system state; After establishing the initial network B0 and the transition network B → After that, through the joint probability distribution P(X0,X1,…,X T ) models the global state of the system from time t = 0 to t = T, and the joint probability distribution is: in, represents the distribution of the initial state, is the conditional probability at time t given all previous states.

7. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1, characterized in that: In the dynamic Bayesian network DBN, the Markov assumption is used to simplify the model, that is, it is assumed that at any time t, the state X at time t+1 t+1 Depends only on X at the current moment t , and is independent of other previous state conditions, simplifying to: P(X0,X 11 ,...,X T )=P(X t+1 |X t ) (12) It is further assumed that the network topology and conditional probability distribution do not change over time between adjacent time steps, that is, P(X t+1 |X t ) is independent of time t.

8. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1, characterized in that: The contents of the migration operation are: Through random migration, some bacteria will randomly choose new locations to increase the exploration range of the solution space; migration occurs with a certain probability Ped, and the migrated bacteria are randomly relocated; after a period of searching, bacteria with higher classification accuracy are copied, and individuals with lower classification accuracy are eliminated; then, by setting the migration probability, bacteria migrate randomly.

9. The method for diagnosing partial discharge faults of reactors based on compressed sensing and dynamic Bayesian network according to claim 1, characterized in that: The specific improvement steps of differential evolution DE include: (1) Chemotaxis operation The chemotaxis operation introduces the bacterial sensitivity V to sense the global optimal position, and accelerates the convergence speed by adaptive step size adjustment, which is expressed by expressions (13)-(14); Where V represents the sensitivity of bacteria to the global optimal solution; J i is the fitness value of the current bacteria; J max is the maximum fitness value in the population; parameter x max and x min They define the upper and lower limits of the optimization search space respectively; rand is the generated random number; C(i) new represents the updated step size of the bacteria in the chemotaxis operation; C(i) is the current step size of the bacteria; step max is the maximum allowed step size defined; step i represents the actual step length taken by the bacteria in the i-th iteration; (2) Mutation Operation In the mutation operation of differential evolution, firstly, two individuals X2(t) and X3(t) in the population that are different from the current individual X1(t) are randomly selected, and the difference vector is generated by calculating their vector difference, and then multiplied by the scaling factor F for adjustment, as shown in expression (15); X1(t+1)=X1(t)+F[X2(t)-X3(t)] (15) (3) Crossover operation The crossover operation controls the gene exchange between individuals through the crossover factor CR. During this process, a dimension irand is randomly selected for forced crossover, and the value of the random number rand is used to determine whether to exchange genes in other dimensions, as shown in expression (16): Among them, CR is the crossover factor, which is used to control the probability of gene exchange between individuals; irand represents the randomly selected dimension index, ensuring that forced crossover is performed on the predetermined dimension; rand is a generated random number, usually in the range of [0,1], which is used to determine whether to perform crossover operations on non-forced dimensions; (4) Select an operation The selection operation adopts a greedy strategy, which determines the retention of individuals by comparing the fitness values ​​of the offspring individual X1(t+1) and the parent individual X1(t); if the fitness of the offspring individual is better than that of the parent, the offspring individual is retained as the parent of the next generation; otherwise, the original parent individual is retained.

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